Font families

Computer Modern: Getting to specifics, the first and still
most prevalent typeface in the TeX world is Computer
Modern, developed by Donald Knuth using his novel Metafont
program, which comes with TeX.

Other Modern: Variants of Computer Modern have been created
which cover letters and symbols from virtually all other Latin-based
languages, as well translating the characters into PostScript Type 1
fonts, etc. Latin
Modern and cm-super
are two notable collections along these lines.

The Utopia
serif typeface has been donated by Adobe. The excellent Fourier-GUT
collection is based on Utopia.

Free OpenType/TrueType-only fonts

These free (libre) fonts do not have Type 1 versions and
therefore are most easily used with XeTeX and LuaTeX. (Some of the
fonts above and below also have OpenType and/or TrueType versions.)
They are all included in the principal TeX distributions.

The getnonfreefonts script simplifies
installation of these fonts, and others. Try
getnonfreefonts --help.

Proprietary typefaces

First, if you are interested in helping produce more free fonts,
please see the GNU Font
Utilities web page and this TUGboat article for starting
points, and let us know.

Excellent fonts are available commercially from many companies.
Unfortunately, the ones we checked (Adobe, Bitstream, et al.) have
extremely high prices for a font library (thousands of dollars). Prices
for individual typefaces are also expensive. There are a number of
inexpensive collections available, of varying quality and legality, but
since none are legally usable everywhere in the world, regrettably TUG
cannot specifically recommend any of them. Commercial fonts typically
do not come with support for TeX, such as .tfm files, but many such
metrics are available on CTAN; see especially Walter
Schmidt's collection and MinionPro TeX
support.

One commercial font collection we can recommend is MathTime Pro 2 by Michael
Spivak, distributed by Personal TeX,
Inc. It has a full complement of Times Roman characters for math
typesetting with TeX, based on original designs. It can be used with
any TeX implementation that supports TeX's virtual
fonts.

Finally, the Lucida typeface family, while
remaining under a proprietary license, is available through TUG,
in both Type 1 and OpenType versions.